Home Page of Alberto Bressan

Position

Information:

• Office: room 201 McAllister Building
• Office phone: (814) 865 1667
• Fax: (814) 865 3735

Teaching and mentoring:

• Math 597A - Nonlinear Partial Differential Equations. Syllabus.

Publications and CV:

• My CV and list of publications .

Books:

• Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem (bookcover.html).
• Introduction to the Mathematical Theory of Control (leaflet.pdf) (a list of misprints.pdf) .
• Lecture Notes on Functional Analysis, with Applications to Linear Partial Differential Equations (bookcover.html) (an updated list of misprints.pdf). For instructors, a complete set of solutions to the 180 homework problems is available upon request.

Most of my papers on hyperbolic conservation laws are available on the NTNU preprint server (Trondheim, Norway).

Areas of current research:

• Hyperbolic conservation laws and nonlinear wave equations
• Modeling and optimization of traffic flow on networks
• Optimal control, non-cooperative games, and applications to economics and finance
• Differential inclusions, dynamic blocking problems
• Impulsive control of Lagrangian systems by means of active constraints

Brief surveys of recent results and open problems:

• Research themes on traffic flow on networks
• Research themes on non-cooperative games and applications
• Research themes on differential inclusions
• Results and open questions on dynamic blocking problems

• 1 - A mixing problem
• 2 - A blocking problem

Slides of recent talks:

• Optima and equilibria for a model of traffic flow
  (pdf-file, 34 pages) (animation: Model 1) (animation: Model 2) (animation: instability of Nash equilibrium, Model 2)
• Dynamic blocking problems
  (pdf-file, 40 pages)
• Controlling Lagrangian systems by active constraints
  (pdf-file, 31 pages)
• A tutorial on hyperbolic systems of conservation laws in one space dimension
  I - Basic concepts (pdf-file, 27 pages)
  II - Solutions to the Cauchy problem (pdf-file, 35 pages)
  III - Uniqueness and continuous dependence (pdf-file, 25 pages)
  IV - Vanishing viscosity approximations (pdf-file, 33 pages)

Some survey papers and tutorials:

• Globally Optimal and Nash Equilibrium Solutions for Traffic Flow on Networks
  Proceedings of the conference HYP2012, Padova.
  (pdf-file, 8 pages)
• Dynamic Blocking Problems
  A survey (2011).
  (pdf-file, 30 pages)
• Noncooperative differential games. A tutorial
  Notes for a Summer course, Padova 2010.
  (pdf-file, 81 pages)
• Hyperbolic conservation laws: an illustrated tutorial
  Notes for a summer course, Cetraro 2009.
  (pdf-file, 81 pages)
• Viscosity solutions of nonlinear hyperbolic systems
  Proceedings HYP2002, Pasadena.
  (pdf-file, 21 pages)
• Hyperbolic systems of conservation laws in one space dimension
  Proceedings International Congress of Mathematicians, Beijing 2002.
  (pdf-file)
• Symmetries and blow up patterns
  A short tutorial, SISSA 1999.
  (pdf-file, 17 pages)
• Viscosity solutions of Hamilton Jacobi equations and optimal control problems
  An illustrated tutorial. Original version: Trondheim, NTNU 2001. Revised: Shanghai Jiao Tong University, 2011.
  (pdf-file, 49 pages)
• Lecture Notes on the Center Manifold Theorem
  S.I.S.S.A., 2003.
  (pdf-file, 16 pages)
• Notes on the Boltzmann equation
  lecture notes for a summer course, S.I.S.S.A., 2005.
  (pdf-file, 28 pages)
• BV solutions to hyperbolic system by vanishing viscosity
  Lecture notes for a C.I.M.E. course, 2003.
  (pdf-file, 77 pages)
• Impulsive control of Lagrangian systems and locomotion in fluids
  (pdf-file, 34 pages)

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Some other papers, preprints:

• On differential systems with vector-valued impulsive control
  (with F.Rampazzo) (pdf-file, 16 pages)
• Extremal selections of multifunctions generating a continuous flow
  (with G.Crasta) (pdf-file, 17 pages)
• On discontinuous differential equations
  (with W.Shen) (pdf-file, 14 pages)
• Optimal control problems on stratified domains
  (with Y.Hong) (pdf-file, 19 pages)
• Trajectories of a differential inclusion with state constraints
  (with G.Facchi) (pdf-file, 15 pages)
• Optima and equilibria for a model of traffic flow
  (with K.Han) (pdf-file, 35 pages)
• Variational analysis of Nash equilibria for a model of traffic flow
  (with C.J.Liu, W.Shen, and F.Yu) (pdf-file, 21 pages)
• On the control of non-holonomic systems by active constraints
  (with K.Han and F.Rampazzo) (pdf-file, 26 pages)
• Existence of optima and equilibria for traffic flow on networks
  (with K.Han) (pdf-file, 23 pages)
• A multi-dimensional optimal harvesting problem with measure valued solutions
  (with G.M.Coclite and W.Shen) (pdf-file, 15 pages)
• Optimal pricing strategies in a continuum limit order book
  (with G.Facchi) (pdf-file, 34 pages)
• Stackelberg solutions of feedback type for differential games with random initial data
  (with D.Wei) (pdf-file, 19 pages)
• Extremal solutions of differential inclusions via Baire category: a dual approach
  (pdf-file, 8 pages)
• Discrete bidding strategies for a random incoming order
  (with G.Facchi) (pdf-file, 20 pages)
• A Bidding Game with Heterogeneous Players
  (with D.Wei) (pdf-file, 23 pages)